Definitely an elm. It appears Ulmus minor is native to SW England so is definitely a candidate.
English elm can also have quite small leaves sometimes depending on the soil, grazing, competition from other plants and other factors.
There are also many other small leaf elms that are used as bonsai and in gardens so some background as to where it came from may help the guesses a bit.
There are two common types of elm in UK Ulmus Minor (field elm) and Ulmus Glabra (wych Elm) and their hybrids.
Field elm has smaller leaves and samaras and suckers from the roots freely, wych elm has larger leaves and samaras and doesn't sucker from the roots as freely. English elm is a cultivar of field elm.
Yours is most likely a Ulmus Minor as stated above
https://www.forestresearch.gov.uk/documents/6447/FCBK042.pdf this is helpful but a bit out of date as it refers to cultivars as species but recent genetic testing has confirmed that they are all cultivars and hybrids of the wych elm and field elm